Scilab Function
Last update : Dec 1997

cdfpoi - cumulative distribution function poisson distribution

### Calling Sequence

  `[P,Q]=cdfpoi("PQ",S,Xlam)`
  `[S]=cdfpoi("S",Xlam,P,Q)`
  `[Xlam]=cdfpoi("Xlam",P,Q,S);`

### Parameters

- `P,Q,S,Xlam`: four real vectors of the same size.
- `P,Q (Q=1-P)` : The cumulation from 0 to S of the poisson density. Input range: [0,1].
- `S`:Upper limit of cumulation of the Poisson. Input range: [0, +infinity). Search range: [0,1E300]
- `Xlam`: Mean of the Poisson distribution. Input range: [0, +infinity). Search range: [0,1E300]

### Description

Calculates any one parameter of the Poisson distribution given values for the others.

Formula 26.4.21 of Abramowitz and Stegun, Handbook of Mathematical Functions (1966) is used to reduce the computation of the cumulative distribution function to that of computing a chi-square, hence an incomplete gamma function.

Cumulative distribution function (P) is calculated directly. Computation of other parameters involve a seach for a value that produces the desired value of P. The search relies on the monotinicity of P with the other parameter.

From DCDFLIB: Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters (February, 1994) Barry W. Brown, James Lovato and Kathy Russell. The University of Texas.